PRINCIPLES OF NAVAL ENGINEERING 



noted above but refer to the values for 1 pound 

 of the working substance rather than to the 

 values for the total quantity of the working sub- 

 stance. In both equations, it should be noted 

 that the subscripts 1 and 2 refer to a separation 

 in time rather than to a separation in space. 



EXAMPLE: Four pounds of working sub- 

 stance are compressed in the cylinder shown 

 in figure 8-7, The process is accomplished 

 without the addition or removal of any heat but 

 with a net increase in total internal energy of 

 120 Btu. Find the work done on or by the work- 

 ing substance, in Btu per pound and in foot- 

 pounds per pound. 



SOLUTION: First arrange the equation to fit 

 the problem, as follows: 



wk 



12 



(ug - Uj) + q 



12 



Since no heat is added or removed, q2^2 = '^• 

 Since U2 - Uj, or the net increase in total in- 

 ternal energy, is equal to 120 Btu, and since we 

 are dealing with 4 pounds of the working sub- 

 120 



stance, uo — Ui = 



= 30 Btu per pound. 



The work done on or by the working sub- 

 stance, in Btu per pound, is given by the ex- 



wk^2 

 pression — i — . Thus, 



wk 



12 



( - 30) + Btu per lb 

 - 30 Btu per lb 



The answer is negative, indicating that the 

 work is done on the working substance rather 

 than by the working substance. 



To find the work done on the working sub- 

 stance in foot-pounds per pound, we merely 



wkj2 

 solve the equation for wk^, rather than for — = — 



and substitute. Thus, 



wkj2 = (-30) (778) = -23, 340 ft-lb per lb 



Again, the negative answer indicates that 

 work is done on_the working substance rather 

 than b^the working substance. 



A steady-flow process is one in which a 

 working substance flows steadily and uniformly 

 through some device. Boilers, turbines, con- 

 densers, centrifugal pumps, blowers, and many 

 other actual machines are designed for steady- 

 flow processes. In an ideal steady-flow process, 

 the following conditions exist: 



1. The properties— pressui-e, temperature, 

 specific volume, etc.— of the working fluid re- 

 main constant at any particular cross section 

 in the flow system, although the properties ob- 

 viously must change as the fluid proceeds from 

 section to section. 



2. The average velocity of the working fluid 

 remains constant at any selected cross section 

 in the flow system, although it may change as 

 the fluid proceeds from section to section. 



3. The system is always completely filled 

 with the working fluid, and the total weight of 

 the fluid in the system remains constant. Thus, 

 for each pound of working fluid that enters the 

 system during a given period of time, there is 

 a discharge of 1 pound of fluid during the same 

 period of time. 



4. The net rate of heat transfer and the work 

 performed on or by the working fluid remain 

 constant. 



In actual machinery designed for steady-flow 

 processes, some of these conditions are not 

 entirely satisfied at certain times. For example, 

 a steady-flow machine such as a boiler or a 

 turbine is not actually going through a steady- 

 flow process until the warming-up period is 

 over and the machine has settled down to steady 

 operation. For most practical purposes, minor 

 fluctuations of properties and velocities caused 

 by load variations do not invalidate the use of 

 steady-flow concepts. In fact, even suchpiston- 

 and-cylinder devices as air compressors and 

 reciprocating steam engines may be considered 

 as steady-flow machines if there are enough 

 cylinders or if some other arrangement is used 

 to smooth out the flow so that it is essentially 

 uniform at the inlet and the outlet. 



The equations for steady-flow processes are 

 based on the general energy equation— that is, 

 energy in must equal energy out. Steady-flow 

 equations are written in various ways, depend- 

 ing upon the forms of energy that are involved 

 in the process under consideration. The forms 

 of energy which, to greater or lesser degree, 

 enter into any general equation for steady-flow 



176 



